A Note on Graphs with Prescribed Orbit Structure

This paper presents a proof of the existence of connected, undirected graphs with prescribed orbit structure, giving an explicit construction procedure for these graphs. Trees with prescribed orbit structure are also investigated.publishedVersionPeer reviewe

A treatment of stereochemistry in computer aided organic synthesis

This thesis describes the author’s contributions to a new stereochemical processing module constructed for the ARChem retrosynthesis program. The purpose of the module is to add the ability to perform enantioselective and diastereoselective retrosynthetic disconnections and generate appropriate precursor molecules. The module uses evidence based rules generated from a large database of literature reactions. Chapter 1 provides an introduction and critical review of the published body of work for computer aided synthesis design. The role of computer perception of key structural features (rings, functions groups etc.) and the construction and use of reaction transforms for generating precursors is discussed. Emphasis is also given to the application of strategies in retrosynthetic analysis. The availability of large reaction databases has enabled a new generation of retrosynthesis design programs to be developed that use automatically generated transforms assembled from published reactions. A brief description of the transform generation method employed by ARChem is given. Chapter 2 describes the algorithms devised by the author for handling the computer recognition and representation of the stereochemical features found in molecule and reaction scheme diagrams. The approach is generalised and uses flexible recognition patterns to transform information found in chemical diagrams into concise stereo descriptors for computer processing. An algorithm for efficiently comparing and classifying pairs of stereo descriptors is described. This algorithm is central for solving the stereochemical constraints in a variety of substructure matching problems addressed in chapter 3. The concise representation of reactions and transform rules as hyperstructure graphs is described. Chapter 3 is concerned with the efficient and reliable detection of stereochemical symmetry in both molecules, reactions and rules. A novel symmetry perception algorithm, based on a constraints satisfaction problem (CSP) solver, is described. The use of a CSP solver to implement an isomorph‐free matching algorithm for stereochemical substructure matching is detailed. The prime function of this algorithm is to seek out unique retron locations in target molecules and then to generate precursor molecules without duplications due to symmetry. Novel algorithms for classifying asymmetric, pseudo‐asymmetric and symmetric stereocentres; meso, centro, and C2 symmetric molecules; and the stereotopicity of trigonal (sp2) centres are described. Chapter 4 introduces and formalises the annotated structural language used to create both retrosynthetic rules and the patterns used for functional group recognition. A novel functional group recognition package is described along with its use to detect important electronic features such as electron‐withdrawing or donating groups and leaving groups. The functional groups and electronic features are used as constraints in retron rules to improve transform relevance. Chapter 5 details the approach taken to design detailed stereoselective and substrate controlled transforms from organised hierarchies of rules. The rules employ a rich set of constraints annotations that concisely describe the keying retrons. The application of the transforms for collating evidence based scoring parameters from published reaction examples is described. A survey of available reaction databases and the techniques for mining stereoselective reactions is demonstrated. A data mining tool was developed for finding the best reputable stereoselective reaction types for coding as transforms. For various reasons it was not possible during the research period to fully integrate this work with the ARChem program. Instead, Chapter 6 introduces a novel one‐step retrosynthesis module to test the developed transforms. The retrosynthesis algorithms use the organisation of the transform rule hierarchy to efficiently locate the best retron matches using all applicable stereoselective transforms. This module was tested using a small set of selected target molecules and the generated routes were ranked using a series of measured parameters including: stereocentre clearance and bond cleavage; example reputation; estimated stereoselectivity with reliability; and evidence of tolerated functional groups. In addition a method for detecting regioselectivity issues is presented. This work presents a number of algorithms using common set and graph theory operations and notations. Appendix A lists the set theory symbols and meanings. Appendix B summarises and defines the common graph theory terminology used throughout this thesis

Kinetic model construction using chemoinformatics

Kinetic models of chemical processes not only provide an alternative to costly experiments; they also have the potential to accelerate the pace of innovation in developing new chemical processes or in improving existing ones. Kinetic models are most powerful when they reflect the underlying chemistry by incorporating elementary pathways between individual molecules. The downside of this high level of detail is that the complexity and size of the models also steadily increase, such that the models eventually become too difficult to be manually constructed. Instead, computers are programmed to automate the construction of these models, and make use of graph theory to translate chemical entities such as molecules and reactions into computer-understandable representations. This work studies the use of automated methods to construct kinetic models. More particularly, the need to account for the three-dimensional arrangement of atoms in molecules and reactions of kinetic models is investigated and illustrated by two case studies. First of all, the thermal rearrangement of two monoterpenoids, cis- and trans-2-pinanol, is studied. A kinetic model that accounts for the differences in reactivity and selectivity of both pinanol diastereomers is proposed. Secondly, a kinetic model for the pyrolysis of the fuel “JP-10” is constructed and highlights the use of state-of-the-art techniques for the automated estimation of thermochemistry of polycyclic molecules. A new code is developed for the automated construction of kinetic models and takes advantage of the advances made in the field of chemo-informatics to tackle fundamental issues of previous approaches. Novel algorithms are developed for three important aspects of automated construction of kinetic models: the estimation of symmetry of molecules and reactions, the incorporation of stereochemistry in kinetic models, and the estimation of thermochemical and kinetic data using scalable structure-property methods. Finally, the application of the code is illustrated by the automated construction of a kinetic model for alkylsulfide pyrolysis

Relationships between symmetry-based graph measures

This paper addresses the problem of comparing different measures of graph symmetry. Two measures, each based on the number and respective sizes of the vertex orbits of the automorphism group or a graph, are compared. A real valued distance measure is used to compare the symmetry measures by establishing the limiting value of the distances for several well known classes of graphs.Peer reviewe

【研究分野別】シーズ集 [英語版]

[英語版

Multicoloured Random Graphs: Constructions and Symmetry

This is a research monograph on constructions of and group actions on countable homogeneous graphs, concentrating particularly on the simple random graph and its edge-coloured variants. We study various aspects of the graphs, but the emphasis is on understanding those groups that are supported by these graphs together with links with other structures such as lattices, topologies and filters, rings and algebras, metric spaces, sets and models, Moufang loops and monoids. The large amount of background material included serves as an introduction to the theories that are used to produce the new results. The large number of references should help in making this a resource for anyone interested in beginning research in this or allied fields.Comment: Index added in v2. This is the first of 3 documents; the other 2 will appear in physic

Cheminformatics for genome-scale metabolic reconstructions

Genome-scale metabolic reconstructions are an important resource in the study of metabolism. They provide both a system and component level view of the biochemical transformations of metabolites. As more reconstructions have been created it remains a challenge to integrate and reason about their contents. This thesis focuses on the development of computational methods to allow on-demand comparison and alignment of metabolic reconstructions. A novel method is introduced that utilises chemical structure representations to identify equivalent metabolites between reconstructions. Using a graph theoretic representation allows the identification and reasoning of metabolites that have a non-exact match. A key advantage is that the method uses the contents of reconstructions directly and does not rely on the creation or use of a common reference. To annotate reconstructions with chemical structure representations an interactive desktop application is introduced. The application assists in the creation and curation of metabolic information using manual, semi-auto\-mated, and automated methods. Chemical structure representations can be retrieved, drawn, or generated to allow precise metabolite annotation. In processing chemical information, efficient and optimised algorithms are required. Several areas are addressed and implementations have been contributed to the Chemistry Development Kit. Rings are a fundamental property of chemical structures therefore multiple ring definitions and fast algorithms are explored. Conversion and standardisation between structure representations present a challenge. Efficient algorithms to determine aromaticity, assign a Kekulé form, and generate tautomers are detailed. Many enzymes are selective and specific to stereochemistry. Methods for the identification, depiction, comparison, and description of stereochemistry are described.The project was funded by Unilever, the Biotechnology and Biological Sciences Research Council [BB/I532153/1], and the European Molecular Biology Laboratory

Applications and Variations of the Maximum Common Subgraph for the Determination of Chemical Similarity

The Maximum Common Substructure (MCS), along with numerous graph theory techniques, has been used widely in chemoinformatics. A topic which has been studied at Sheffield is the hyperstructure concept - a chemical definition of a superstructure, which represents the graph theoretic union of several molecules. This technique however, has been poorly studied in the context of similarity-based virtual screening. Most hyperstructure literature to date has focused on either construction methodology, or property prediction on small datasets of compounds. The work in this thesis is divided into two parts. The first part describes a method for constructing hyperstructures, and then describes the application of a hyperstructure in similarity searching in large compound datasets, comparing it with extended connectivity fingerprint and MCS similarity. Since hyperstructures performed significantly worse than fingerprints, additional work is described concerning various weighting schemes of hyperstructures. Due to the poor performance of hyperstructure and MCS screening compared to fingerprints, it was questioned whether the type of maximum common substructure algorithm and type had an influence. A series of MCS algorithms and types were compared for both speed, MCS size, and virtual screening ability. A topologically-constrained variant of the MCS was found to be competitive with fingerprints, and fusion of the two techniques overall improved active compound recall

Comparing graphs

Graphs are a well-studied mathematical concept, which has become ubiquitous to represent structured data in many application domains like computer vision, social network analysis or chem- and bioinformatics. The ever-increasing amount of data in these domains requires to efficiently organize and extract information from large graph data sets. In this context techniques for comparing graphs are fundamental, e.g., in order to obtain meaningful similarity measures between graphs. These are a prerequisite for the application of a variety of data mining algorithms to the domain of graphs. Hence, various approaches to graph comparison evolved and are wide-spread in practice. This thesis is dedicated to two different strategies for comparing graphs: maximum common subgraph problems and graph kernels. We study maximum common subgraph problems, which are based on classical graph-theoretical concepts for graph comparison and are NP-hard in the general case. We consider variants of the maximum common subgraph problem in restricted graph classes, which are highly relevant for applications in cheminformatics. We develop a polynomial-time algorithm, which allows to compute a maximum common subgraph under block and bridge preserving isomorphism in series-parallel graphs. This generalizes the problem of computing maximum common biconnected subgraphs in series-parallel graphs. We show that previous approaches to this problem, which are based on the separators represented by standard graph decompositions, fail. We introduce the concept of potential separators to overcome this issue and use them algorithmically to solve the problem in series-parallel graphs. We present algorithms with improved bounds on running time for the subclass of outerplanar graphs. Finally, we establish a sufficient condition for maximum common subgraph variants to allow derivation of graph distance metrics. This leads to polynomial-time computable graph distance metrics in restricted graph classes. This progress constitutes a step towards solving practically relevant maximum common subgraph problems in polynomial time. The second contribution of this thesis is to graph kernels, which have their origin in specific data mining algorithms. A key property of graph kernels is that they allow to consider a large (possibly infinite) number of features and can support graphs with arbitrary annotation, while being efficiently computable. The main contributions of this part of the thesis are (i) the development of novel graph kernels, which are especially designed for attributed graphs with arbitrary annotations and (ii) the systematic study of implicit and explicit mapping into a feature space for computation of graph kernels w.r.t. its impact on the running time and the ability to consider arbitrary annotations. We propose graph kernels based on bijections between subgraphs and walks of fixed length. In an experimental study we show that these approaches provide a viable alternative to known techniques, in particular for graphs with complex annotations